, .
2 + + 2 +D x + E y + F = 0, (6)
2 + 2 + 2 ¹ 0 (.. , , ). 2, , 2 ,
d =
. (6) .
:
: Þ = , = 0, = , D = = 0, F = 1,
d = . >0;
2 + 2 = 2 Þ = = 1, = D = = 0, F = 2, d = 1>0;
: Þ = , = 0, = , D = = 0, F = 1,
d = . < 0.
: 2 = 2 Þ = = 0, =1, D = 2 , = F = 0, d = 0,
2 = 2 Þ = 1 = = D = 0, = 2 , F = 0, d = 0.
, (6), , d¹0. d> 0, , d<0, . , d = 0 .
, . (, (6)), , , (5). , (, ) . , (6) , , .
.
I. ( ). (, ), ¢ ( ¢, ¢). ,
(7), (8).
(7) (8) .
II. a. (, ), ¢ ( ¢, ¢).
, (9)
(6) .
1) ,
2) ,
3) 2 = 2 , 2 = 2
4) 2 2 b 2 y 2 = 0 (. )
5) y 2 a 2 = 0 (. )
6) x 2 a 2 = 0 (. )
7) y 2 = 0 ( )
8) x 2 = 0 ( )
9) 2 2 + b 2 y 2 = 0 (0, 0)
10)
11) y 2 + a 2 = 0
12) x 2 + a 2 = 0 .
|
|
. , 4 12, .
.
1) 9 2 + 4 2 54 + 8 + 49 = 0 Þ (9 2 54 ) + (4 2+ 8 ) + 49 = 0 Þ
9( 2 6 + 9) + 4( 2 + 2 + 1) 81 4 + 49 = 0 Þ 9( 3)2 + 4( + 1) = 36, Þ
.
¢ = 3, ¢ = + 1, . ¢ = 3, ¢ = + 1 (3, 1). , .
2) 3 2 +4 12 +8 = 0. :
(3 2 12 )+ 4 +8 = 0
3( 2 4 +4) 12 + 4 +8 = 0
3( 2)2 + 4( 1) = 0
( 2)2 = ( 1).
¢ = 1, ¢ = 2, ¢2 = ¢. ¢(1,2).
, ( , ) ¢ = 3, ¢ = 2, .. : (3, 2) (3, 2) .
, ¢, .
3) 4 2 2 + 8 + 6 5 = 0 Þ
4 2+ 8 2+ 6 5 = 0,
4( 2+ 2 +1) ( 2 6 +9)4 +9 5 = 0,
4( +1)2 ( +3)2 = 0.
¢ = +1, ¢ = 3 4 ¢2 ¢2 = 0 ¢¢¢, ¢(1, 3).
¢ = 2 ¢
.
4) 2 + 2 + 2 4 = 0 Þ ( 2 + 2 + 2) 4 = 0,
( + )2 4 = 0 Þ ( + 2)( + +2) = 0,
+ 2 = 0 + +2 = 0
, . , ¢ 2 2 = 0,
¢ 2 2 = 0.